Because it's not a prediction stat, it's relative to how good a player is right now. ERA+ takes performance and adjusts to make all outside factors even. If you want correlation for future seasons, you don't use ERA+. I used ERA+ because it's past performance that Lincecum is being signed for, and ERA+ is the most unbiased measure of recent performance.

The correlation article is looking at actual data from actual seasons that actually happened. It's looking at what pitchers did in certain consecutive seasons to see which stats are more stable and which are more prone to large fluctuations even when other things point to the pitcher performing more or less the same. It can be useful for trying to predict future performance, but those correlations are not calculated from an unknown future performance. Those are based on how good a pitcher has been and is right now.

I would argue that ERA+ is good at telling how many runs a pitcher gave up in a way that normalizes it to ballpark and competition, but that the Giants are not basing the contract they gave to Lincecum solely on that aspect of his past performance. ERA+ can fluctuate (just like actual ERA) significantly and be impacted by strange things, and the Giants probably are looking deeper than that and saying that when looking at a bigger picture, Lincecum's recent past performance isn't as bad as a glance at ERA+ might say it was.